Talk:Barrelled space
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Bornographic?
[edit]I never heard of the word bornographic but I know bornological, a term that also was introduced by Burbaki. Maybe that's what is meant here? --131.234.106.197 12:05, 11 October 2007 (UTC)
- Removed that. Stca74 (talk) 09:21, 18 March 2008 (UTC)
E.g.
[edit]So what's a good example of a barrel in an NLS not containing the origin? Any simple proofs for some of these statements? —vivacissamamente (talk) 07:34, 29 March 2008 (UTC)
you might want to link to
[edit]http://de.wikipedia.org/wiki/Tonnelierter_Raum 84.191.233.176 (talk) 13:18, 4 July 2008 (UTC)
Baire spaces
[edit]@Vincer 17: it's not correct to say that all Baire spaces are barreled, because not all Baire spaces are topological vector spaces. Eozhik (talk) 07:35, 3 July 2018 (UTC)
@Eozhik: Of course you are right. My only quibble was with local convexity; I have now edited it in a way that I hope is satisfactory.
@Vincer 17: to tell the truth, Baire space sounds better in this place, because one can give a link to the corresponding Wikipedia article. Eozhik (talk) 12:47, 4 July 2018 (UTC)
Conflation of barrelled and ultrabarrelled spaces.
[edit]For several of the equivalent properties the reference Adasch, Ernst & Keim 1978 is used, but they use "barrelled" to mean a property that is more usually referred to as "ultrabarrelled" (see e.g. Ultrabarrelled space). This is not equivalent to "barrelled" as defined in this article, so I believe the characterisations 3-6 are incorrect. To make them correct, I believe it is mostly enough to impose that Y is locally convex. In addition, they are correct if X is assumed locally convex (since then "barrelled" and "ultrabarrelled" coincide).
But I am not an expert, so this may all be wrong. ~2026-22030-6 (talk) 11:09, 11 January 2026 (UTC)